Abstract
We propose a two-grid algorithm for implementation of a generalized A.M.Il’in’s scheme to a system of semilinear diffusion convection-dominated equations. To solve the nonlinear algebraic system of difference equations we use Newton method. We derive the difference scheme on a coarse mesh and, then using uniform interpolation, taking into account the boundary layers, we obtain the initial guess for an iterative method on a fine mesh. Estimates of the accuracy and the computational work are obtained. The main advantage of the proposed algorithm is the computational cost.
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Vulkov, L.G., Zadorin, A.I. (2009). A Two-Grid Algorithm for Solution of the Difference Equations of a System of Singularly Perturbed Semilinear Equations. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_68
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DOI: https://doi.org/10.1007/978-3-642-00464-3_68
Publisher Name: Springer, Berlin, Heidelberg
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